Everyone assumes that broad asset class diversification in an investment portfolio is advantageous. The major benefit is to reduce the risk associated with events that can trigger a decline in any one asset class. By holding a variety of asset classes that are mostly uncorrelated with one another, the investor hopes to avoid those catastrophic occurrences that completely wipes out years of gains such as what happened during the credit crisis of 2008. Further, diversification makes financial planning more reliable and predictable by reducing the variations in portfolio performance from year to year.

Simply put, diversification is a sound investment practice.

But exactly how much risk reduction, in actual numbers, is obtained through application of this philosophy? That was the question I was pondering and was wondering if, indeed, asset class diversification is all that it’s cracked up to be.

Let’s find out.

[Disclaimer: First of all, nothing that follows is an attempt to challenge the precept of broad diversification as an indispensable investment tool, so don’t get scared. Consider this analysis to be an exercise in quantitatively determining the relevance of just how much risk can be reduced by adding more asset classes to one’s portfolio.]

Setup

The ideal tool for performing the analysis in this article is Modern Portfolio Theory (MPT). This Nobel Prize winning approach utilizes complex mathematics to tell you how to best allocate your funds among various asset classes to minimize risk.

Risk can be looked at as fluctuations in portfolio returns. In MPT, risk is measured by a statistical term called the standard deviation. It is this quantity that MPT seeks to minimize in recommending portfolio allocations. [The software used in the analyses conducted here is the SMC Analyzer. Click here for more info.]

The portfolios considered here used monthly total return data taken from January 1928 through May 2011 for each of the following ten asset classes:

1. Large-cap U.S. Stocks
2. Small U.S. Stocks
3. Long-Term Corporate Bonds
4. Long-Term Government Bonds
5. Intermediate-Term Government Bonds
6. 30-day U.S. Treasury Bills
7. Real Estate Investment Trusts (REITs)
8. International Stocks
9. International Bonds
10. Gold

Each of these asset classes are themselves composed of a broad diversification of assets within that class. This article does not address that need, only the benefits of diversification among various classes.

Baseline

The methodology used in this analysis was to first establish a baseline return/risk table using all ten candidate asset classes (Table 1 below). You’ll see that the table contains certain measures of risk defined as follows:

1. Standard Deviation – statistical measure of portfolio return fluctuation around the target return
2. Probability of Loss – chance of that portfolio losing value in any one year
3. Sharpe Ratio – a measure of risk versus reward with larger numbers being better

This baseline data is shown in Table 1 along with the current ten asset class portfolio allocations (through May 2011.)

Table 1. Baseline portfolio incorporating all ten candidate asset classes.

(Click to enlarge.)

Methodology

The next step was to remove each asset class one by one in each of successive rounds and to assess its effect on the measures of risk. At the end of each round we chose to eliminate that asset class that increased the measures of risk the least [sentence corrected]. This was repeated for eight rounds until only two asset classes remained. Eliminations required examination of 52 separate portfolios (10+9+8+7+6+5+4+3).

By using the above measures of risk as our benchmark, asset classes were eliminated from consideration in each successive round in the following order:

1. International Bonds
2. Long-Term Government Bonds
3. Real Estate Investment Trusts
4. Gold
5. International Stocks
6. 30-day U.S. Treasury Bills
7. Large U.S. Stocks
8. Either Intermediate-Term Government Bonds or Long-Term Corporate Bonds depending on target return

Results

Tables 2a and 2b show the measures of risk using only two asset classes in the MPT analysis. There are two tables because different asset class combinations are preferable for the most conservative portfolios (target returns up to and including 7%) and the more aggressive ones (target returns 8% and above).

Table 2a. Two asset class allocations and risk measures for conservative portfolios

Required	Standard	Probability	Sharpe	Small	Medium-Term
Annual	Deviation	Of	Ratio	Company	Government
Return		Loss		Stocks	Bonds
5.5%	4.6%	0.12	1.19	1.8%	98.2%
6.0%	5.3%	0.13	1.14	10.1%	89.9%
7.0%	8.7%	0.21	0.81	25.0%	75.0%

Table 2b. Two asset class allocations and risk measures for more aggressive portfolios

Required	Standard	Probability	Sharpe	Small	Long-Term
Annual	Deviation	Of	Ratio	Company	Corporate
Return		Loss		Stocks	Bonds
8.0%	12.8%	0.27	0.62	34.3%	65.7%
9.0%	17.3%	0.30	0.52	50.4%	49.6%
10.0%	22.4%	0.33	0.45	66.3%	33.7%
11.0%	27.8%	0.35	0.40	82.1%	17.9%
12.0%	33.6%	0.36	0.36	97.8%	2.2%
12.1%	34.4%	0.36	0.35	100.0%

You can see from the tables that returns are best realized by small-cap stocks and medium-term government bonds in conservative portfolios, and by small-cap stocks and long-term corporate bonds (investment grade) in the more aggressive ones. The inclusion of small-cap stocks especially in the more aggressive portfolios should come as no surprise because it is this asset class that is capable of generating the highest returns over the long haul. In fact, it is because of using only small-cap stocks to generate returns in the two candidate model that returns below 5.5% are completely unachievable (but so are very low levels of risk).

Now let’s see how these results compare to the classical model of using ten asset classes.

Comparison of results

Table 3 presents the risk differences associated with reducing ten asset classes to only two.

Table 3. Risk difference between two and ten asset classes

Required	Standard	Probability	Sharpe
Annual	Deviation	Of	Ratio
Return		Loss
6.0%	0.2%	0.01	-0.04
7.0%	0.4%	0.01	-0.03
8.0%	0.4%	0.01	-0.03
9.0%	0.5%	0.00	-0.02
10.0%	0.6%	0.01	-0.01
11.0%	0.7%	0.01	-0.01
12.0%	0.2%	0.00	0.00

Discussion

What this analysis shows is truly astonishing and surprising. You can see that the reduction in the number of asset classes has a relatively insignificant effect on risk. I’m betting few folks would have expected this result!

To summarize all this into one number, you are increasing your overall level of portfolio risk by only about 1 part in 20 by decreasing the number of candidate asset classes from ten all the way down to two. This is based on the general numerical increase in the values of the risk measures as measured from their baselines.

An historical comparison

Looking at this from a historical perspective, let’s see how well a portfolio with only two asset classes would have fared against a traditional portfolio with all ten. Table 4 shows the results of actually following the recommended MPT allocations–with monthly rebalancing–from January of 1928 through May of 2011.

Table 4. Comparison of actual returns achieved utilizing ten asset classes versus two asset classes.

Required	Ten Asset Classes		Two Asset Classes		Differences
Return	Return	SD	Return	SD	Return	SD
6.0%	7.1%	7.3%	8.0%	8.9%	0.9%	1.6%
7.0%	8.2%	10.1%	9.1%	11.1%	0.9%	1.0%
8.0%	8.6%	12.6%	10.2%	13.5%	1.6%	0.9%
9.0%	9.1%	14.5%	10.9%	15.7%	1.8%	1.2%
10.0%	10.1%	16.7%	11.4%	17.6%	1.3%	0.9%
11.0%	10.9%	18.8%	11.7%	19.2%	0.8%	0.4%
12.0%	11.8%	19.9%	11.8%	20.5%	0.0%	0.6%

 [To read this table, the Return under each model is the actual return the portfolio would have realized at the required return level given in the first column, and SD is the risk defined by the standard deviation.]

Let’s look at an example. To achieve a 10% required compounded average annual return, a ten candidate asset class portfolio would have achieved its goal and would have actually returned 10.1% at a risk of 16.7%. That same 10% targeted return attempted using only two asset classes would have actually produced a greater return, 11.4%, with only a slightly higher standard deviation of 17.6%.

It is interesting to note that the portfolios composed of only two asset classes exceeded their targets more so than their ten asset class counterparts. This is due to the fewer choices available to the mathematics of MPT in its attempts to achieve, at least, the required return while also minimizing the level of risk. But in so doing, the level of resultant risk is commensurately slightly higher.

Conclusion

The takeaway from this article should be to note that it doesn’t take broad asset class diversification to adequately achieve one’s investment goals with a reasonable level of reward versus risk. So all of you lazy Lisas and Larrys out there can sleep easier knowing that your nest egg needn’t be diversified among more than the two carefully selected asset classes discussed above for you to realize your desired long-term return at minimum risk.

There are also some practical advantages of choosing the two asset class approach over the ten asset class model. One is the amount of time and inconvenience it may take to rebalance many asset classes every month. The other, and possibly more important advantage, is the amount of coin you might save in trading fees. That alone could well justify the small increase in risk!

In a follow up article we’ll see if we can get away with reducing the number of asset classes in MPT portfolios that include market timing.

Pat Glenn contributed to this article.

This entry was posted on Thursday, July 14th, 2011 at 3:48 pm and is filed under Modern Portfolio Theory related articles. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.